1. Search for fan clubs devoted to the person you're looking for.
2. Contact a musician by looking for a contact address in a CD or cassette booklet or looking up the address of the record company that released the recording.
3. Contact a screen actor or actress through the Screen Actors Guild.
4. Contact a director through the Directors Guild of America.
5. Contact a stage actor or actress through the theater at which he or she is currently performing or has recently performed.
6. Contact a television or radio personality in care of the station or network that he or she works for.
7. Contact authors and literary editors through the National Writers Union or through their publishers.
8. Contact a famous athlete in care of his or her team.
9. Contact an artist through a gallery or museum that houses his or her work.

via ehow

1. Look up the celebrity's official web page on the Internet.
2. Go to your local library and look for the 'Star Directory'. .
3. Check the person's Internet Movie Database page . 
4. Search the Internet for autograph collecting sites and forums.
5. Write a nice, short letter. 
6. Include a SASE.
7. Consider including something to sign.
8. Use the right envelope and adequate postage.
9. Be patient.
10. Keep your head high.

via wikihow

1. Start with a fan website search.
2. Research at http://www.imbd.com/.
3. Make a request through the agent.
4. Prepare a letter or email.
5. Make a simple request. 
6. Provide a return address and envelope.
7. Be patient.

via howtodothings